Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #487 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,13)(12,14)(16,17,19,21)(18,23,22,20);(8,10,11,15)(9,12,13,14)(17,20)(18,22)(21,23);(2,3)(4,5)(6,7)(8,9,11,13)(10,14,15,12)Polycyclic presentation:
2^6,7|a^2=e,b^2=e,c^2=f,d^2=f,b^a=be,c^a=ce,g^a=g^6,c^b=cd,d^b=df,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89564, #11736230, #11736250, … |
| maximal normal subgroup of | C2×#89564, #11736230, #11736250, … |
| maximal quotient of | #11726557, #11726565, #11726597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 326);